M13-09

Question

If a bacterial colony doubles every day at 9 a.m. and loses 320 bacteria every day at 9 p.m., what was the population size of the colony at 8 a.m. on Day 3 if exactly 320 bacteria were lost at 9 p.m. on Day 5, resulting in extinction of the colony?

A. 160
B. 240
C. 280
D. 480
E. 560

Show Answer

Official Answer

C

A. 160
B. 240
C. 280
D. 480
E. 560

Bunuel · Answer

Official Solution:

If a bacterial colony doubles every day at 9 a.m. and loses 320 bacteria every day at 9 p.m., what was the population size of the colony at 8 a.m. on Day 3 if exactly 320 bacteria were lost at 9 p.m. on Day 5, resulting in extinction of the colony?

A. 160
B. 240
C. 280
D. 480
E. 560

Show Answer

Official Answer

C

A. 160
B. 240
C. 280
D. 480
E. 560

Suppose the size of the colony at 8 a.m. on Day 3 was  x  bacteria;
 
At 9 a.m. on Day 3 it would become  2x  and at 9 p.m. of the same day it would become  2x - 320 ;
 
At 9 a.m. on Day 4 it would become  2(2x - 320)  and at 9 p.m. of the same day it would become  2(2x - 320) - 320 ;
 
At 9 a.m. on Day 5 it would become  2*(2(2x - 320) - 320)  and at 9 p.m. of the same day it would become  2*(2(2x - 320) - 320) - 320 ;
 
Since at that point the colony was extinct, then  2*(2(2x - 320) - 320) - 320=0 .
 
Solving gives  x = 280

Answer: C

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

sssdd1234 · Answer

I think this is a  high-quality  question and I agree with explanation.

Hitesh0701 · Answer

Hi Bunuel,
Can we do reverse calculation and arrive at the answer?

Bunuel · Answer

We are told the bacterial colony doubles every day at 9 a.m. and loses 320 bacteria every day at 9 p.m. On Day 5 at 9 p.m., exactly 320 bacteria are lost and the colony becomes extinct. We are asked to find the size of the colony at 8 a.m. on Day 3.

We work backward from the extinction point:

9 p.m. Day 5: colony is extinct, so population = 0
Before losing 320: population must have been 320

9 a.m. Day 5: population = 320
 Before doubling at 9 a.m.: population = 160

9 p.m. Day 4: population = 160
 Before losing 320: population = 480

9 a.m. Day 4: population = 480
 Before doubling at 9 a.m.: population = 240

9 p.m. Day 3: population = 240
 Before losing 320: population = 560

9 a.m. Day 3: population = 560
 Before doubling at 9 a.m.: population = 280

So, the population at 8 a.m. on Day 3 was 280.

Answer: C.

Orange2020 · Answer

I think the reverse calculation approach is the best approach because it is time efficient and reduces possibilities of mistakes between steps.

The algebraic approach introduces many layers of calculations which can go wrong at any step, especially under time pressure.

nandini14 · Answer

How do we know that on day 5 the colony will be extinct?

Bunuel · Answer

It’s written directly in the question:  “resulting in extinction of the colony.”  So the colony becomes extinct on Day 5. Read the question carefully.

Adit_ · Answer

This question is wicked, saying 8am on Day 3 so basically doubling is yet to happen and thus it is 280 and not 560, to those that got wrong (including me, silly me)

This question deserves to be under hard section IMO because of the tricky option.

M13-09

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